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CFA Level I · CFA Level I Exam

Pricing and Valuation of Futures Contracts for CFA Level I

Futures and forward pricing rests on no-arbitrage: the contract price must equal the spot price grown at the risk-free rate, adjusted for carry costs and benefits. Solve it by finding the forward price at initiation, then value the contract later as the present value of the price difference.

What this chapter covers

This chapter shows how to price and value forwards and futures without guessing the future. The core idea is no-arbitrage. If two ways of getting the same payoff cost different amounts, a riskless profit exists, and trading removes it. So the forward price is fixed by the spot price, the risk-free rate, and the costs and benefits of holding the asset.

You move from pricing to valuation. Pricing sets the forward price at initiation so the contract has zero value. Valuation asks what the contract is worth later, once spot prices, time and rates have changed. These are different questions, and the exam tests the difference often. You then apply the same logic to interest rate forwards and FX forwards, and finish with how futures differ from forwards.

The chapter links to several other areas. It builds on time value of money from Quantitative Methods and on the basic derivative definitions in the earlier Derivatives chapters. It supports Fixed Income (forward rates), Portfolio Construction (hedging and currency exposure) and Equities (index and dividend effects). The same no-arbitrage thinking returns in options pricing.

Derivatives and Risk Management carries a lower topic weight (6-9%) than some other topics, but this chapter is among its most calculation-driven and predictable. Questions are standalone three-option MCQs with a short formula, so a candidate who knows the structure can often answer a short formula question within the suggested 90 seconds. The same ideas also help in Fixed Income and Portfolio Construction questions. With no penalty for wrong answers and no minimum score per topic, secure marks here are efficient to earn.

Pricing and Valuation of Futures Contracts: topics in the order to study them

  1. 1Principles of No-Arbitrage PricingEverything else uses this logic, so learn the law of one price, arbitrage and the carry-and-replicate idea first.
  2. 2Pricing of Forward and Futures ContractsIt gives the core formula for the forward price at initiation, with carry costs and benefits, before you add time.
  3. 3Valuation of Forward Contracts Over TimeValuation after initiation builds directly on the pricing formula and needs you to separate price from value.
  4. 4Pricing Interest Rate and FX Forwards and FuturesThese apply the same formulas to rates and currencies, so they come once the basic mechanics are solid.
  5. 5Futures vs Forwards and Spot-Futures RelationshipsIt closes the chapter by comparing the two contracts and linking the spot-futures relationship to carry, which needs all the earlier ideas.

How to prepare Pricing and Valuation of Futures Contracts

Most marks come from a few formulas used correctly, so build understanding first and then practise short MCQs under time.

  1. Read the no-arbitrage idea until you can explain in your own words why a mispriced forward lets you earn a riskless profit, and what you would buy and sell.
  2. Write the forward price formula for each case on one page: no carry, with a known cost or benefit, with continuous compounding, and for FX. Say what each term means in plain words.
  3. Practise valuation separately. For a long forward, value = St − F0 ÷ (1 + r)^(T − t) when there is no carry. With carry, use St − PV(benefits) + PV(costs) − F0 ÷ (1 + r)^(T − t). Always check whether the question asks for price or value.
  4. Use your calculator for the exponent and discounting steps. On the TI BA II Plus, use the yx key for (1 + r)^t and eˣ (2ND, LN) for continuous compounding. On the HP 12C, use the yx key and keep rates in decimals.
  5. Draw a small timeline for each FX and interest rate problem. Mark the domestic and foreign currency, and check that the rate and time units match.
  6. Do mixed sets of standalone MCQs. For each, eliminate two options by checking direction: does carry raise or lower the forward price, and does the sign of the value make sense?
  7. In the last days, redo missed questions and re-derive each formula once from the no-arbitrage argument instead of only memorising it.

Common mistakes in Pricing and Valuation of Futures Contracts

  • Confusing the forward price with the forward value.

    Fix: Remember that price is fixed at initiation and makes value zero. Value changes afterwards. Check the question wording before choosing a formula.

  • Adding dividends or benefits to the spot price instead of subtracting their present value.

    Fix: Ask who holds the asset. The holder gets the benefit, so it reduces the cost of carrying and lowers the forward price. Costs do the reverse.

  • Inverting the FX forward formula.

    Fix: Write the quote as domestic per foreign first. Put the domestic rate in the numerator and the foreign rate in the denominator. Then check the direction: if the domestic rate is higher, F must be greater than S, so the foreign currency is at a forward premium and the domestic currency at a discount.

  • Mixing discrete and continuous compounding or mismatching time units.

    Fix: Convert time to years and use the compounding the question gives. Use the same method for the whole problem.

  • Getting the sign wrong on a short position's value.

    Fix: Calculate the long value, then flip the sign for the short. Check that the gain direction matches how spot moved.

  • Assuming futures and forwards always have the same price.

    Fix: State the condition: they are approximately equal only when interest rates are uncorrelated with futures prices. Daily settlement is what creates the difference.

Last-day revision: Pricing and Valuation of Futures Contracts

  • No-arbitrage: two payoffs that are identical must cost the same, otherwise a riskless profit exists.
  • Forward price with no carry: F0 = S0 × (1 + r)^T, or S0 × e^(rT) with continuous compounding.
  • Storage costs and other holding costs raise the forward price; benefits such as dividends or convenience yield lower it.
  • With a known benefit, F0 = (S0 − PV of benefits + PV of costs) × (1 + r)^T.
  • A forward has zero value at initiation, because the forward price is set to make it so.
  • Long forward value before expiry (no carry): Vt(long) = St − F0 ÷ (1 + r)^(T − t). With carry: Vt(long) = St − PV(benefits) + PV(costs) − F0 ÷ (1 + r)^(T − t).
  • At expiry, long forward value = ST − F0; short forward value is the negative of that.
  • FX forward (covered interest rate parity): F = S × (1 + r domestic) ÷ (1 + r foreign), with S quoted as domestic per foreign.
  • If the domestic rate is higher than the foreign rate, F > S (domestic per foreign): the foreign currency is at a forward premium and the higher-rate domestic currency is at a forward discount.
  • Forward rate logic: the forward rate f is the rate for the later period that makes investing at the longer-term rate equal to investing at the shorter-term rate and then rolling over at the forward rate: (1 + r_long)^T2 = (1 + r_short)^T1 × (1 + f)^(T2 − T1).
  • Futures are marked to market daily and traded on exchanges; forwards are private and settle at maturity.
  • If interest rates are uncorrelated with futures prices, forward and futures prices are approximately equal.

Pricing and Valuation of Futures Contracts practice questions

Pricing and Valuation of Futures Contracts in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Pricing and Valuation of Futures Contracts: frequently asked questions

How is a forward price different from forward value?

The forward price is the agreed delivery price, set at initiation so the contract has zero value. The value is what the contract is worth later, after spot and rates change. It is found by comparing the current spot position with the present value of the forward price.

Do I need to memorise many formulas for this chapter?

You need a small set, and they all come from one idea: no-arbitrage. Learn the base formula and how carry costs, benefits and the foreign rate modify it. If you can derive them, you will recall them under pressure.

How should I use my calculator for futures pricing questions?

You mainly need powers and the exponential function. On the TI BA II Plus, use the yx key and 2ND then LN for eˣ. On the HP 12C, use the yx key and enter rates as decimals. Always check units before pressing keys.

Why does the higher-interest-rate currency trade at a forward discount?

Under covered interest rate parity, no-arbitrage requires the forward rate to offset the interest rate gap. With S as domestic per foreign, a higher domestic rate makes F greater than S, so the foreign currency is at a forward premium and the higher-rate domestic currency is at a forward discount. This removes any riskless profit from borrowing in the low-rate currency and investing in the high-rate one.